Question

Help please!
Use the Mean Value Theorem to
1) Find the point c on (a,b) at which the tangent line of the following function is parallel to the secant line
2) Write an equation for the tangent line

f(x)=-x^2+6x [1,4]

Answer 1

so you know you need this:
\[f'(c)=\frac{f(b)-f(a)}{b-a}\]

Answer 2

f'(c) tells you to find the derivative of f
and then evaluate f' at c


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b tells you to plug in 4
a tells you to plug in 1

Answer 3

Okay I got f'(x) -2x+6 and [f(4)-f(1)]/3 = 1. And x=7/2

Answer 4

so -2x+6=1
-2x=1-6 right

Answer 5

1-6 isn't -7 but -5 right?

Answer 6

i think you know that

-2x=-5
so x=5/2 not 7/2

Answer 7

so you are asked to find the tangent line to the point (5/2,f(5/2)) to the curve f=-x^2+6x

Answer 8

so you do this:

y-f(5/2)=f'(5/2)*(x-5/2)

you need to find f(5/2) and also f'(5/2)

Answer 9

I got f'(5/2)=1 and f(5/2)=35/4. So my final answer is y-(35/4)=x-(5/2)

Answer 10

looks great

Answer 11

Thank you so much

Answer 12

np you did all the work