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Find the tangent line to f(x)=x^1/4 When x=625. Find the y values on that tangent line when x=621 andthen when x=635 and finally when x=1450?
1 Answer
- 7 years ago
Find derivative first:
f(x) = x^1/4
f'(x) = (1/4)x^-3/4
f'(x) = 1/(4x^(3/4))
Plug in to find slope:
1/(4(625)^3/4) = 1/(4(125)) = 1/500
To find the tangent line, you need a point. Plug x into original:
f(x) = (625)^1/4 = 5
(625, 5)
Use slope and the point to find y-intercept (b):
y = mx + b
5 = (1/500)(625) + b
5 = (1.25) + b
3.75 = b
15/4 = b
Your equation is y = (1/500)x + (15/4)
Just plug in x values to find the rest:
y = (1/500)(621) + (15/4) = 621/125 = 4.992
y = (1/500)(635) + (15/4) = 251/50 = 5.02
y = (1/500)(1450) + (15/4) = 133/20 = 6.65
