How do you find the slope of a tangent line to the graph of the function # f(x) = 2e^(-3x)# at (0, 2)?

Answer 1

#f'(0)=-6#

#f(x)=2e^(-3x)# Use the exponent rule to differentiate #f(x)#: #f'(x)=(-3)(2)(e^(-3x))# #f'(x)=-6e^(-3x)#
#f'(0)=-6e^[-3*0]=-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 2

To find the slope of a tangent line to the graph of a function at a specific point, you can use the derivative of the function. In this case, the function is f(x) = 2e^(-3x). To find the slope of the tangent line at the point (0, 2), you need to find the derivative of f(x) and evaluate it at x = 0.

The derivative of f(x) = 2e^(-3x) can be found using the chain rule. The derivative is given by f'(x) = -6e^(-3x).

To find the slope of the tangent line at x = 0, substitute x = 0 into the derivative: f'(0) = -6e^(-3(0)) = -6e^0 = -6.

Therefore, the slope of the tangent line to the graph of f(x) = 2e^(-3x) at the point (0, 2) is -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