MATH265 Arizona State University Equation of The Tangent Line Questions please check the attached questions that you will need to show all of steps needed to solve them Use linear approximation, i.e. the tangent line, to approximate 25.1 as follows:

Let f(x) = Vc. The equation of the tangent line to f(x) at x = 25 can be written in the form y

= mx + 6

where m is:

and where b is:

Using this, we find our approximation for 25.1 is

NOTE: For this part, give your answer to at least 9 significant figures or use fractions to give the exact

answer

#10 Points possible: 10. Total attempts: 0

Let y =

tan(5x + 3).

Find the differential dy when x = 4 and dx = 0.1

Find the differential dy when 3 = 4 and dx

0.2

#11 Points possible: 10. Total attempts: 0

Find the critical numbers of the function f(x)

12×5 75×4 + 40×3 6 and classify them.

x=

X=

is a Select an answer

is a Select an answer

is a Select an answer

x=

#12 Points possible: 10. Total attempts: 0

Find the maximum and minimum values of the function g(0) =

20 3 sin(() on the interval (0, 7]

Minimum value =

Maximum value =

#13 Points possible: 10. Total attempts: 0

The function f(x) = 5 + 6x + 150x has one local minimum and one local maximum.

This function has a local maximum at x =

with value

and a local minimum at x =

with value

Given f(x) = 2V + 5, find f'(x) using the limit definition of the derivative.

f'(x)=

#5 Points possible: 10. Total attempts: 0

5 In()

Differentiate: y =

24

y’

=

#6 Points possible: 10. Total attempts: 0

Let

11x

f(2)

sin x + cos2

=

f'(-1) =

#7 Points possible: 10. Total attempts: 0

6.02 + 5x + 2

If f(2)=

then:

ve

? ?

f'(x) =

f'(3) =

#8 Points possible: 10. Total attempts: 0

If f(x) = 5x sin x cos x, find f'(x).

Find f'(5).

/#14 Points possible: 10. Total attempts: 0

Consider the function f(x) = 4 6×2 on the interval [ 2,5). Find the average or mean slope of the

function on this interval, i.e.

f(5) – f(-2)

5- (-2)

=

By the Mean Value Theorem, we know there exists a c in the open interval ( 2,5) such that f'(c) is equal

to this mean slope. For this problem, there is only one c that works. Find it.

#15 Points possible: 10. Total attempts: 0

Consider the function f(x) = 2.03 9×2

slope of the function on this interval.

24x + 1 on the interval [ 4,7]. Find the average or mean

By the Mean Value Theorem, we know there exists a c in the open interval ( 4, 7) such that f'(c) is equal

to this mean slope. For this problem, there are two values of c that work. The small one is

and the larger one is

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