# How do you find the instantaneous rate of change of the function #F(x) = e^x# when x=0?

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

To find the instantaneous rate of change of the function ( F(x) = e^x ) when ( x = 0 ), you can calculate the derivative of ( F(x) ) with respect to ( x ) and then evaluate it at ( x = 0 ). The derivative of ( e^x ) is itself, so ( F'(x) = e^x ). Evaluating this derivative at ( x = 0 ) gives the instantaneous rate of change at that point, which is ( F'(0) = e^0 = 1 ). Therefore, the instantaneous rate of change of ( F(x) = e^x ) when ( x = 0 ) is 1.

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

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.

- How do you find the average rate of change of #f(x)= x^3 + 1# over the interval (2,3) and (-1,1)?
- How do you find the equation of a line tangent to the function #y=x^2-2# at x=0?
- What is the average value of the function #g(x) = cosx# on the interval #[0, pi/2]#?
- How do you find the equation of the tangent and normal line to the curve #y^3-3x-2y+6=0# at (9,3)?
- What is the equation of the line tangent to #f(x)=(x-3)^2# at #x=4#?

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