- #1
Jacobpm64
- 239
- 0
Given y = f(x) with f(1) = 4 and f'(1) = 3, find
(a) [tex] g'(1) if g(x) = \sqrt {f(x)} [/tex]
(b) [tex] h'(1) if h(x) = f(\sqrt {x}) [/tex]
(a) [tex] g'(x) = \frac {1}{2} f(x)^\frac{-1}{2} * f'(x) [/tex]
[tex] g'(1) = \frac {1}{2} f(1)^\frac{-1}{2} * f'(1) [/tex]
[tex] g'(1) = \frac {1}{2}(4)^\frac{-1}{2} * 3 [/tex]
[tex] g'(1) = \frac {3}{4} [/tex]
(b) [tex] h'(x) = f'(\sqrt{x}) [/tex]
[tex]h'(1) = f'(\sqrt{1}) [/tex]
[tex]h'(1) = f'(1) [/tex]
[tex]h'(1) = 3 [/tex]
Are these correct?
I'm not sure if this was the correct approach.
Thanks.
(a) [tex] g'(1) if g(x) = \sqrt {f(x)} [/tex]
(b) [tex] h'(1) if h(x) = f(\sqrt {x}) [/tex]
(a) [tex] g'(x) = \frac {1}{2} f(x)^\frac{-1}{2} * f'(x) [/tex]
[tex] g'(1) = \frac {1}{2} f(1)^\frac{-1}{2} * f'(1) [/tex]
[tex] g'(1) = \frac {1}{2}(4)^\frac{-1}{2} * 3 [/tex]
[tex] g'(1) = \frac {3}{4} [/tex]
(b) [tex] h'(x) = f'(\sqrt{x}) [/tex]
[tex]h'(1) = f'(\sqrt{1}) [/tex]
[tex]h'(1) = f'(1) [/tex]
[tex]h'(1) = 3 [/tex]
Are these correct?
I'm not sure if this was the correct approach.
Thanks.
Last edited: