Question

Consider the function f(x)=x3+4x2+2. find the points where the tangent line is horizontal.

Answer 1

Thinking about the graph of f(x), the rate of change is zero whenever there is an extremum.

First, differentiate f(x)


`f'(x)=3x^2+8x`

Next, find the zeros of f'(x) by factoring.


`x(3x+8)=0 \\ x= (-8)/(3),x=0`

Now, we substitute these x-values into the original equation to find the coordinates.

(-2.667, 11.481), (0, 2)