AP Calculus ABmediummcq1 pt

An equation of the line tangent to the graph of f(x)=5x43x2+7f(x)=5x^4-3x^2+7 at x=1x=1 is

A.y9=14(x1)y-9=14(x-1)
B.y9=14(x1)y-9=-14(x-1)
C.y7=14(x1)y-7=14(x-1)
D.y9=20(x1)y-9=20(x-1)

Explanation

Core Concept

Here f(x)=20x36xf'(x)=20x^3-6x, so f(1)=14f'(1)=14, and f(1)=53+7=9f(1)=5-3+7=9. The point-slope form gives y9=14(x1)y-9=14(x-1).

Correct Answer

Ay9=14(x1)y-9=14(x-1)

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