Brief Calculus.

Question

Use Calculus to show the x-values where the tangent line is horizontal

f (x) = e^{x^3-4x^2-8x+10}

Answer 1

The tangent line is horizontal only when f'(x) = 0.

So, e^{x^3 - 4x^2 - 8x + 10}(3x²-8x-8) = 0

e to a power is always positive, so 3x²-8x-8 = 0

Use the quadratic formula to solve for x.