Need Help On Calculus

Just got back to school yesterday and working on my homework. Unfortunately my professor doesn't explain things too well so I am stuck on what to do.

Can anybody help?

I've attached the problems. So far I did the first two problems and got 0 and -2 as answers.

 

Uhhhh 12? Bump

 

You are correct for the first two.

 

I found online that the equation for the tangent to the curve at point (1,4) is...

y=6-2x

But I don't know how to get that.

 

Thanks! Good to know I did the easy part right haha

 

For 10(a), derivative is -2x

At (1,4), x = 1, so slope is -2(1) = -2

Tangent line's slope is also -2, so y = -2x+b.

Sub in (1,4) for x,y: 4 = -2(1)+b >>> b = 6

Tangent line is therefore y = -2x + 6

 

^ winner winner, someone get this man some chicken for dinner.

 

Using the chain rule you find that y'=-2x and which tells you the slope at point (1,4) is y'(1)=-2. Now that you have the slope and the point which the line goes through (1,4) you can use point slope form to get the equation of your tangent line.

edit: ^^Looks like I just got beat

 

average rate of change for a function is:

{f(b) - f(a)}/(b-a)

so for the first problem it woulb be

(1^2) - (-1^2) / (-1-1) = 0

 

How did you find the derivative? I've been trying to get that.

 

Multiply the x's coefficient with the exponent, reduce the exponent by 1.

-x^2's derivative is therefore -2x^1

 

I can't see attachment but is the starting eq f (x):= -x^2 +5? If so slope is derivative: -2x and at point x:=1 then m:= -2. Use point slope formula y-y1=m (x-x1) and fill in the blanks(x1, y1) and solve for y.

 

dy/dx = -2 ...the slope is a constant...

 

Here's my answers for the last problem (number 12) using the great info you guys game me...

(a) f'(x) = 2(x-2)
f'(1) = -2

(b) y-(-3) = -2(x-1)
y+3 = -2x+2
y = -2x-1

How's it look?

 

looks right to me HI TRD, ....ready for us to start assigning some problems to solve?

 

You guys start school before Labor Day? Interesting.

 

My god I am not looking forward to going back to more college.

 

School started on Monday for us. It usually starts a week earlier.

 

Haha thanks! I think I have enough to keep me busy

Yah yesterday was the first day. I didn't even realize Labor Day is next Monday.

 

Big Mahalo to everyone for helping me out!

I'm sure I will be posting more problems here as the semester goes on, so please stay sub'd