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Determine the point(s) on the following function where the tangent line is horizontal:f(x)=−x3+3x2option-(−1,2)(0,0)(1,2)(2,4)

Question

Determine the point(s) on the following function where the tangent line is horizontal:
f(x)=−x3+3x2
option-
(−1,2)
(0,0)
(1,2)
(2,4)

check_circleAnswer
Step 1

f(x)=−x3+3x2

In order to get the slope of the curve or that of a tangent to the curve at any point (x, y) we need to differentiate the function with resepct to x.

Step 2

Recall the famous rule of differentiation:

d(xn) / dx = nxn-1

Step 3

Let's apply this rule to our function, f(x)=−x3+3x2

f'(x) = -3x2 + 3.2.x = -3x2 +...

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Tagged in

Math

Calculus

Derivative

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