What is the equation of the line tangent to #f(x)= 2x^3+8x # at #x=-1#?

Answer 1

#y+24=14(x+1)#, or, if you prefer slope-intercept form, the equation is #y=14x-10#

#f(x) = 2x^3+8x#
At #x= -1#, we have #y=f(-1) = 2(-8)+8(-1) = -16-8 = -24#.
So the tangent line contains the point #(-1,-24)#
#f'(x) = 6x^2+8#, so the slope of the tangent at the point where #x= -1# is
#m = f'(-1) = 6(1)+8 = 14#
The line through #(-1, -24)# with slope #m=14# has equation:
#y+24=14(x+1)#.
If you prefer slope-intercept form, the equation is #y=14x-10#
Sign up to view the whole answer

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

Sign up with email
Answer 2

The equation of the line tangent to f(x) = 2x^3 + 8x at x = -1 is y = -2x - 6.

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7