Question 2 Consider the function f(x) = 4e®³-1. i) Find f(1) and f'(1). ii) Let f(1) = Yo be your answer from part (i). Using the Inverse Function Theorem, find (f-1)'(yo). iii) Verify your answer to part (ü) by explicitly finding f-1 and compute (f-1)'(yo).

Q: Evaluate f''(c) at the point. f(x) = (x2 - 4)(x3- 2), c = 1

A:

Q: Differentiate the function f(x) +5r DO NOT simplify or factor %3D (7-z)31 quotient 012 Your answer…

A: We have to find derivative

Q: A shopper buys cat food in bags of 3 lbs. Her cat eats 3434 lb each week. How many weeks does one…

A: Given that A shopper buys cat food in bags of 3 lbs. Her cat eats 3/4 lb each week

Q: How long will it take to drive 700 km at 100 km per hour, if you take a 1-hour break after every 5…

A: We have to find time taken to drive 700km using given data. We will use formulaes,…

Q: represents

A: False

Q: Show that f-(A U B) = f-'(A) U f-'(B) and f-1(A n B) = f-'(A) nf-'(B) for any function f. Is the…

A:

Q: what for is the symbolic representa f(x), f(x) = 8x X+7 Find the inverse f='(x) = of f.

A:

Q: Solve: 2 0 -1 0 2 -6 1 -2 -3 -2 0 1 -5

A:

Q: f(x) = 2 sec (-) + 1 2

A:

Q: If f is one-to-one and f( – 3) = 12, then f-'(12) and (f( – 3))¯

A:

Q: x2 – 4 x2 - 9 Consider the function f (x) a) Find f' and f" and simplify both.

A: Given,           fx=x2-4x2-9

Q: Suppose f and g are one-to-one functions such that f(2) = 7, f(4) = 2, and g(2) = 5. Find the value,…

A: We have given functions f and g are one-to-one. Then, a. gof-17=gf-17=g2=5 b. fog-15=fg-15=f2=7

Q: Composites of Functions

A: As per company guidelines, I can solve only first three subpart.

Q: Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.

A: It is given that f''(a)=0 at (a, f(a)). The objective is to explain and sketch how a function can…

Q: Determine whether the inverse of f is a function. Then find the inverse. Ax) - Ae) - O no; f-(x) =6/…

A: We have to find the inverse of functions

Q: Let f(x) = ∥x∥. Find out its conjugate function f ⋆ and prove your conclusion.

A:

Q: For each of the following 1-1 functions f(x), determine the inverse function f-1 (x) stating the…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.