Posted by Karen on Monday, August 4, 2014 at 7:37pm.
Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the following equation of f '(x).
f '(x) = y0 − y/x0 − x
f(x) = √x
(x0, y0) = (-16, 0)
Calculus - Damon, Monday, August 4, 2014 at 7:51pm
y = x^.5
y' = .5 x^-.5
sketching this I am going to reverse slope equation
y' at tangent = m = (y-yo) /( x-xo) = .5x^-.5
y' = m = (y-0)/(x+16) = .5 x^-.5
x^.5 /(x+16) = .5 x^-.5
x/(x+16) = .5
x = .5 x + 8
.5 x = 8
x = 16
so the tangent hits the curve at x = 16
where y = 4 so at
so this line goes through
(-16,0) and (16,4)
You can take it from there I am sure.
Answer This Question
More Related Questions
- Calculus - find an equation of the tangent line to the graph of the function f ...
- Calculus - 1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the ...
- Math- calculus - Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an...
- calculus - 1. Which of the following expressions is the definition of the ...
- calculus - The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b...
- Calculus - The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), ...
- calculus - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...
- Math--Calculus - Let y = f(x) be the continuous function that satisfies the ...
- cal - find the equation of a quadratic function whose graph is tangent at x=1 to...
- calc - The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is...