Question

For what value(s) of x does the graph of f(x)=8x^3+12x^2-144x+24 have a horizontal tangent

Answer 1

The graph of f(x) = 8x^3 + 12x^2 - 144x + 24 has a horizontal tangent at x = -6 and x = 2.

Step-by-step explanation:

To find the values of x for which the graph of f(x) = 8x^3 + 12x^2 - 144x + 24 has a horizontal tangent, we need to find the x-values where the derivative of f(x) is equal to zero. The derivative of f(x) can be found by differentiating each term of the function. Taking the derivative, we get f'(x) = 24x^2 + 24x - 144. Setting this equal to zero, we can solve the quadratic equation to find the x-values:

1. x = -6
2. x = 2

Therefore, the graph of f(x) will have a horizontal tangent at x = -6 and x = 2.

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