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What is the average gradient of a curve between two points A and C?
What is the average gradient of a curve between two points A and C?
- The gradient of the curve at point C
- The difference in y-coordinates of points A and C
- The gradient of the tangent to the curve at point A
- The gradient of the straight line passing through points A and C (correct)
What is the formula for the average gradient of a curve between points P(a, f(a)) and Q(a + h, f(a + h))?
What is the formula for the average gradient of a curve between points P(a, f(a)) and Q(a + h, f(a + h))?
- (f(a + h) - f(a))/h (correct)
- (f(a + h) - f(a))/a
- (f(a + h) + f(a))/h
- (f(a + h) × f(a))/h
What is the purpose of the concept of average gradient in calculus?
What is the purpose of the concept of average gradient in calculus?
- To describe the rate of change of a curve between two points (correct)
- To calculate the gradient of a curve at a single point
- To find the maximum value of a function
- To find the equation of a curve
In the derivation of the average gradient formula, what happens to the value of h?
In the derivation of the average gradient formula, what happens to the value of h?
What is the gradient of the curve g(x) = x^2 at point P(a, g(a))?
What is the gradient of the curve g(x) = x^2 at point P(a, g(a))?
What is the average gradient of the line AC with points A(x_A, y_A) and C(x_C, y_C)?
What is the average gradient of the line AC with points A(x_A, y_A) and C(x_C, y_C)?
What is the average gradient of the curve between points A and C, given points A(x_A, y_A) and C(x_C, y_C)?
What is the average gradient of the curve between points A and C, given points A(x_A, y_A) and C(x_C, y_C)?
What does the average gradient of a curve represent?
What does the average gradient of a curve represent?
Given points P(a, f(a)) and Q(a + h, f(a + h)) on a curve, what is the expression for the average gradient?
Given points P(a, f(a)) and Q(a + h, f(a + h)) on a curve, what is the expression for the average gradient?
In the derivation of the average gradient formula, what is the role of point Q(a + h, f(a + h))?
In the derivation of the average gradient formula, what is the role of point Q(a + h, f(a + h))?
What happens to the value of h in the average gradient formula?
What happens to the value of h in the average gradient formula?
What is the relationship between the average gradient and the gradient at a point?
What is the relationship between the average gradient and the gradient at a point?
What is the main difference between the gradient of a curve and the average gradient of a curve?
What is the main difference between the gradient of a curve and the average gradient of a curve?
Given a curve f(x) with points P(a, f(a)) and Q(a + h, f(a + h)), what is the expression for the average gradient in terms of a and h?
Given a curve f(x) with points P(a, f(a)) and Q(a + h, f(a + h)), what is the expression for the average gradient in terms of a and h?
If the average gradient of a curve f(x) between points P(a, f(a)) and Q(a + h, f(a + h)) is 2a + h, what is the curve f(x) equivalent to?
If the average gradient of a curve f(x) between points P(a, f(a)) and Q(a + h, f(a + h)) is 2a + h, what is the curve f(x) equivalent to?
What is the significance of the point Q(a + h, f(a + h)) in the derivation of the average gradient formula?
What is the significance of the point Q(a + h, f(a + h)) in the derivation of the average gradient formula?
What happens to the value of the average gradient as the distance between points P and Q approaches zero?
What happens to the value of the average gradient as the distance between points P and Q approaches zero?
Given a curve g(x) = x^2, what is the average gradient between points P(a, g(a)) and Q(a + h, g(a + h)) in terms of a and h?
Given a curve g(x) = x^2, what is the average gradient between points P(a, g(a)) and Q(a + h, g(a + h)) in terms of a and h?
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