Posted by erika on Monday, February 28, 2011 at 11:49pm.
Start with defining the function:
f(x)=ax²+bx+c
Find its derivative:
f'(x)=2ax+b
1. f'(1)=8 =>
2a(1)+b = 8 ....(1)
2. f'(-2)=-4 =>
2a(-2)+b = -4 ...(2)
Solve system of equations (1) and (2) for a and b. (a=2,b=4)
The parabola is tangent to the line y=-8 => y=-8 is the minimum.
Now find the minimum of f(x) by setting f'(x)=0 and solve for x.
f'(x)=2ax+b=0
2(2)x+(4)=0
x=-1
So
f(-1)=-8
2(-1)²+4(-1)+c = -8
so c=-6
=>
f(x) = 2x²+4x-6
Do some checking to make sure the function satisfies all the conditions (and in case I make an arithmetic error):
given conditions to be checked:
f(1)=8
f(-2)=-4
minimum f(x)=-8
find the slope of the tangent line to the graph of e^xy=x at (1,0)
write an equation of the tangent line
Related Questions
cal - find the equation of a quadratic function whose graph is tangent at x=1 to...
calculus - 1. Let y = f(x) be the continuous function that satisfies the ...
calculus - 1. Let y = f(x) be the continuous function that satisfies the ...
Math--Calculus - Let y = f(x) be the continuous function that satisfies the ...
Calculus - 55. Find an equation of the tangent line to the graph of f(x) =x^3 - ...
Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...
Calculus - Find the slope m of the tangent line to the graph of the function at ...
Calculus PLEASE HELP - Find the slope m of the tangent line to the graph of the ...
calculus - for the function f(x)=4x^2 +7, find the equation of the tangent line ...
calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...
For Further Reading
