12:35 ll 86% Assignment 1 Cal - Read-only ビy Read Only - You can't save changes to this fi... Show sufficient work to demonstrate understanding. Provide clear work and answers; your an- swers need not be simplified however. Each numbered or lettered response is equally weighted. 1. Find f'(t) if f(t) = dy if y = dx = VIn x 2. Find 3. Find (2tant) dy if y = sec dx (4) 4. Find 5. Find y if y = log(cot x) dy 6. Find if y = tan dt 1 of 3 II 12:35 l 86% Assignment 1 Cal - Read-only ビy Read Only - You can't save changes to this fi... 11. A large spherical snowball is melting. Its volume is decreasing at a rate of 100 cm³ /hr. How fast is the radius of the snowball decreasing when the radius is 25 cm? Note: Be sure to include the appropriate units in your response. Recall that the volume, V, of a sphere of radius r is given by V = ar. x² + 1 12. Let f(x) Show sufficient work in determining ... (a) the intervals over which f is increasing, the intervals over which f is decreasing, and any local extrema. Be sure to indicate whether an extremum is a maximum or a minimum. (b) the intervals over which the graph of f is concave up, those over which it is concave down, and any inflection points. 13. Find the absolute maximum obtained by s(t) = 2t3 – 3t² – 36t +5 on the interval [0,4]. You must show sufficient work for credit here. II

Q: What is the local maximum values of f(x)=x-6/x^2

A: To find point of local maximum/minimum value, Put f'(x) = 0 and solve for x. The obtained value of x…

Q: f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on…

A: Refer  to the question the provided function is f(x) = 4x^3-(x+9)^1/2.

Q: Verify that the given function y is a solution of the differential equation that follows it. Assume…

A:

Q: What is y-intercept of f(x)=2^z

A: The objective is to find the y-intercept of the function fx=2x

Q: Find the value a that will make f(x)={2x^2-7x+3/x-3  if x is not equal to 3…

A:

Q: X f(x) Find A^2f(2) a. 18 b. 6 C. 12 d. 24 0 0.5 1 0 2 O 3 5.5 4 23.0 01 5 118

A: We have to find the value of ∆2y(2) using the table x01234     5f(x)0.5005.523 118

Q: If f(x) = /x – 1, which shows fx)?

A:

Q: Determine the interval(s) for which f(x)=96x^2-x^4  is concave up.

A: Given function is: fx=96x2-x4 Differentiating we get, f'x=ddx96x2-x4f'x=962x-4x3f'x=192x-4x3

Q: Let f(x)=(2^x-2^-x)/2 and g(x)=(2^x+2^-x)/2.  Compute f^2-g^2.

A: in this question f(x) and g(x) is given f(x)=2x-2-x2 g(x)=2x+2-x2 we have to find f(x)2-g(x)2

Q: For f(x)=x^3+3x+1, find exactly f^-1 (2), accurate to two decimal places.

A: Let f-1(2) = a Hence, f(a) = 2 Hence, a3 + 3a +1 = 2 Or, a3 + 3a - 1 = 0

Q: limit as t-0 ((e^-2t)-1)/t,t^7/(t^8-t^7),-8/(2+t)

A:

Q: Let f(x)=-2x/x-1, find f^-1(x)

A:

Q: g(t)=t^{3}+4 t

A:

Q: Determine the target at x=1 F(x) =x ÷root x^2 +1

A:

Q: Find all extreme value (if any) of f(x)=3x^½ + x, on the interval [-1/27, 1/27]

A:

Q: f(x)=sqrt(x+1) find f(t^2-1)

A: We have to find the function

Q: Is the function given by f(x)=x^2+3x/2x-1 continuous over its domain?

A:

Q: N = f(t) = 5000exp(-1/12(t-40)^2) is the form for number of infections, where t = 40 is the peak a)…

A: Let's find.

Q: Plz asap

A:

Q: Find the equation of the slant asymptote for the function f(x)=x^2-x/x-2 y=

A:

Q: At which interval of x is the function of P(x)=(sqrt(1-x^2)) discontinous?

A:

Q: Let f(x)=9-x f^-1(x)=

A:

Q: F(t)= t square-root 9-t^2. (-1,3) Find absolute maximum and minimum values

A:

Q: h(t)=(t^4-9)^3 (t^3+8)^4 What is h(t)=?

A:

Q: f(x)=2(9)^(x+1)=5 on what interval is the function positive

A:

Q: If f(t)=(t^2+6t+2)(7t^2+5). find f'(t) and f'(4)

A: Given: f(t)=t2+6t+27t2+5

Q: If f(t)=(t^2+4t+8)(7t^2+2). find f'(t) and f'(1).

A: Please refer the attached image for complete solution.

Exponential Growth Model

The relation that represents an exponential function is: