# Calculus Optimization Problem Help!?

Please help me get the answer to these problems! I know how to find the absolute min and max when the question gives me a function, but how can I find the answer without a function?

Please explain

Thank you so much!

1) Given f (3) = 7 and f ′(3) = -1.2, approximate Δf if x increases by 0.03.

2)The measurement of the edge of a cube is found to be 5 cm, with a possible error of 0.05 cm inch. Use differentials to estimate the propagated error in computing the surface area of the cube.

3)Suppose f (0) = 9, f ′(0) = 2, and f ″(0) = -4. If df is used to approximate Δf when Δx = 0.01, which of the following would be true?

### 1 Answer

- 6 years agoFavorite Answer
f(3 + 0.03) - f(3)

Describe a tangent line to f(3)

y - 7 = -1.2 * (x - 3)

Now, evaluate f(3.03)

y - 7 = -1.2 * (3.03 - 3)

y - 7 = -1.2 * 0.03

y - 7 = -0.036

y = 6.964

6.964 - 7 = -0.036

It decreases by -0.036 (roughly)

A = 6s^2

s = 5 +/- 0.05

A = 6 * (5 +/- 0.05)^2

A = 6 * (25 +/- 10 * 0.05 + 0.0025)

A = 6 * (25.0025 +/- 0.5)

A = 6 * 25.5025 , 6 * 24.5025

A = 153.015 , 147.015

Don't know for number 3, because I'm certain there were supposed to be some options listed.