# At what points on the graph of #f(x)=2x^3-9x^2-12x+5# is the slope of the tangent line 12?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the points on the graph where the slope of the tangent line is 12, we need to find the derivative of the function f(x) and then set it equal to 12.

The derivative of f(x) is f'(x) = 6x^2 - 18x - 12.

Setting f'(x) equal to 12, we have:

6x^2 - 18x - 12 = 12.

Now, rearrange and solve for x:

6x^2 - 18x - 24 = 0.

Now, solve this quadratic equation to find the values of x. Once you have the values of x, plug them back into the original function f(x) to find the corresponding y-values. These (x, y) points represent where the slope of the tangent line is 12 on the graph of f(x).

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you use the limit definition to find the slope of the tangent line to the graph #f(x) = 2x+4# at (1, 6)?
- What is the equation of the line normal to # f(x)=(x^2-x)(x-2) # at # x=1#?
- How do you find f'(x) using the definition of a derivative for #f(x)= -7x^2 + 4x #?
- How do you find f'(x) using the definition of a derivative for #f(x)=e^x #?
- What is the equation of the line normal to # f(x)=xe^(sqrtx)# at # x=1#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7