Question

attempt 1: 10 attempts remaining. for which values of $x$ does the graph of $f(x)=2x^{3}-54x - 6$ have a horizontal tangent? enter your answers $x$ to 4 places of accuracy. solutions:

Explanation:

Step1: Find the derivative

The derivative of $f(x)=2x^{3}-54x - 6$ using the power - rule $(x^n)'=nx^{n - 1}$ is $f'(x)=6x^{2}-54$.

Step2: Set the derivative equal to zero

A horizontal tangent occurs when $f'(x) = 0$. So we set $6x^{2}-54 = 0$.
First, factor out a 6: $6(x^{2}-9)=0$. Then, we have $x^{2}-9=(x + 3)(x - 3)=0$.

Step3: Solve for x

Setting each factor equal to zero gives $x+3 = 0$ or $x - 3=0$. So $x=-3$ or $x = 3$.

Answer:

$x=-3.0000,x = 3.0000$