At the indicated point, find the slope of the tangent to the curve.
A) -25
B) 133
C) 10
D) 17
E) -53

Question

At the indicated point, find the slope of the tangent to the curve. ​  ​
A) -25 
B) 133 
C) 10 
D) 17 
E) -53

Quizplus · Accepted Answer

The slope of the tangent line at a point on the curve is given by the derivative of the function at that point. Using the power rule, we first find the derivative of the function:
f(x) = -3x^5 + 4x^3 - 9x + 3
f'(x) = -15x^4 + 12x^2 - 9
To find the slope of the tangent line at x = 2, we substitute x = 2 into the derivative:
f'(2) = -15(2)^4 + 12(2)^2 - 9 = -480 + 48 - 9 = -441
Therefore, the slope of the tangent line at x = 2 is -441, which corresponds to answer choice E.

At the Indicated Point, Find the Slope of the Tangent