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11Let f(x) 43x and point P = | 2,7=10a. Use the following definition of the slope of the tangent line at x a to find the slope of the line tangent to the graph of f at P.f(a h) f(a)mtan limh-0h

Question

Hello,

I am struggling to find the slope of the tangent line for the attached problem.

Thanks.

1
1
Let f(x) 43x and point P = | 2,7
=
10
a. Use the following definition of the slope of the tangent line at x a to find the slope of the line tangent to the graph of f at P.
f(a h) f(a)
mtan lim
h-0
h
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1 1 Let f(x) 43x and point P = | 2,7 = 10 a. Use the following definition of the slope of the tangent line at x a to find the slope of the line tangent to the graph of f at P. f(a h) f(a) mtan lim h-0 h

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check_circleAnswer
Step 1

To determine the slope of the tangent line using the definition of the slope at x = a.

Step 2

Given:

1
Function:f(x) 4+3x
Point: P 2
10
Definition of slope: m.. = lim (a+h)-f(a)
h
'tan
h0
-19
help_outline

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1 Function:f(x) 4+3x Point: P 2 10 Definition of slope: m.. = lim (a+h)-f(a) h 'tan h0 -19

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Step 3

Calculate the slope of the tangent line at the point P = (2, 1/10).

Substitute 2 + ...

1
f(2+h) +3(2+h)
1
4 6 3/h
1
10 3h
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1 f(2+h) +3(2+h) 1 4 6 3/h 1 10 3h

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Tagged in

Math

Calculus

Limits

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