If f(3)=8 and f'(3)=-4, then how do you use linear approximation to estimate f(3.02)?
The linear approximation of
So, in point slope form, the tangent line has equation
In this problem, we have
By signing up, you agree to our Terms of Service and Privacy Policy
Using linear approximation, we can estimate ( f(3.02) ) as follows:
[ f(3.02) \approx f(3) + f'(3) \cdot (3.02 - 3) ]
[ \approx 8 + (-4) \cdot (3.02 - 3) ]
[ \approx 8 + (-4) \cdot (0.02) ]
[ \approx 8 - 0.08 ]
[ \approx 7.92 ]
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.
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.
- Given #f(x)=sqrtx# when x=25, how do you find the linear approximation for #sqrt25.4#?
- How do you find the linearization of #f(x)=cosx# at x=5pi/2?
- What will the dimensions of the resulting cardboard box be if the company wants to maximize the volume and they start with a flat piece of square cardboard 20 feet per side, and then cut smaller squares out of each corner and fold up the sides to create the box?
- How do you find the points on the parabola #y = 6 - x^2# that are closest to the point (0,3)?
- How do you minimize and maximize #f(x,y)=x^2+y^3# constrained to #0<x+3xy<4#?

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