Questions and Answers
What is the average gradient of a curve between two points A and C?
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 purpose of the concept of average gradient in calculus?
In the derivation of the average gradient formula, what happens to the value of h?
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What is the gradient of the curve g(x) = x^2 at point P(a, g(a))?
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What is the average gradient of the line AC with points A(x_A, y_A) and C(x_C, y_C)?
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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)?
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What does the average gradient of a curve represent?
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Given points P(a, f(a)) and Q(a + h, f(a + h)) on a curve, what is the expression for the average gradient?
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In the derivation of the average gradient formula, what is the role of point Q(a + h, f(a + h))?
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What happens to the value of h in the average gradient formula?
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What is the relationship between the average gradient and the gradient at a point?
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What is the main difference between the gradient of a curve and the average gradient of a curve?
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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?
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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?
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What is the significance of the point Q(a + h, f(a + h)) in the derivation of the average gradient formula?
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What happens to the value of the average gradient as the distance between points P and Q approaches zero?
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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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