Directions: Consider the following function f(x). f(x) = 4x - 5x Part 1 - Difference Quotient...

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Directions: Consider the following function f(x). f(x) = 4x³ - 5x Part 1 - Difference Quotient If h0, then the difference quotient can be simplified into the form A + Bh+ Ch² That is: f(x+h)-f(x) h = A + Bh+ Ch² where the coefficients A, B, and C can be functions of a or just constant terms. Find these coefficients: A = -5 (Note: It's possible for one or more of these coefficients to be 0.) f'(x) = 12x^2-5 B = -5 Part 2 - Derivative Use the simplified expression from Part 1 to then calculate the derivative f'(x): f(a+h)-f(x) h C = 4 f'(x) = lim h-0 Directions: Consider the following function f(x). f(x) = 4x³ - 5x Part 1 - Difference Quotient If h0, then the difference quotient can be simplified into the form A + Bh+ Ch² That is: f(x+h)-f(x) h = A + Bh+ Ch² where the coefficients A, B, and C can be functions of a or just constant terms. Find these coefficients: A = -5 (Note: It's possible for one or more of these coefficients to be 0.) f'(x) = 12x^2-5 B = -5 Part 2 - Derivative Use the simplified expression from Part 1 to then calculate the derivative f'(x): f(a+h)-f(x) h C = 4 f'(x) = lim h-0

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The given function is fx 4x3 5x The task is to find the coefficients A B and C in the difference quo... View the full answer