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)

Step 1

f(x)=−x^{3}+3x^{2}

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(x^{n}) / dx = nx^{n-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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