SOLUTION: Can someone please help me solve this questions 1. Find dy/dx for y = 5x^2 – 6x + 3 2. What is the tangent line to y = 5x^2 – 6x + 3 at (0,3)? 3. If it exists, what is Lim

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please help me solve this questions 1. Find dy/dx for y = 5x^2 – 6x + 3 2. What is the tangent line to y = 5x^2 – 6x + 3 at (0,3)? 3. If it exists, what is Lim      Log On


   

Question 963782: Can someone please help me solve this questions
1. Find dy/dx for y = 5x^2 – 6x + 3
2. What is the tangent line to y = 5x^2 – 6x + 3 at (0,3)?
3. If it exists, what is Lim (f(3 +h) – f(3)) / h ?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.dy%2Fdx=10x-6
.
.
2. Slope of the tangent line is equal to the value of the derivative at (0,3).
dy%2Fdx=10x-6
m=dy%2Fdx=10%280%29-6
m=-6
Use the point slope form of a line,
y-3=-6%28x-0%29
highlight%28y=-6x%2B3%29
.
.
3. I'm assuming that f%28x%29=5x%5E2-6x%2B3
f%28h%2B3%29=5%28h%2B3%29%5E2-6%28h%2B3%29%2B3
f%28h%2B3%29=5%28h%5E2%2B6h%2B9%29-6h-18%2B3
f%28h%2B3%29=5h%5E2%2B24h%2B30
f%283%29=5%283%29%5E2-6%283%29%2B3
f%283%29=45-18%2B3
f%283%29=30
So then,
f%28h%2B3%29-f%283%29=5h%5E2%2B24h%2B30-30
f%28h%2B3%29-f%283%29=5h%5E2%2B24h
%28f%28h%2B3%29-f%283%29%29%2Fh=5h%2B24
lim%28h-%3E0%2C%28f%28h%2B3%29-f%283%29%29%2Fh=24%29
This is the definition of the derivative at x=3
As a check,
dy%2Fdx=10x-6
dy%2Fdx=10%283%29-6
dy%2Fdx=30-6
dy%2Fdx=24