Differentiating the function $f(x) = x - rac{1}{2}(x + 6)^{rac{1}{2}}$ with respect to $x$:
To find the derivative, we apply the rules of differentiation - Leaving Cert Mathematics - Question b, c - 2015
Question b, c
Differentiating the function $f(x) = x - rac{1}{2}(x + 6)^{rac{1}{2}}$ with respect to $x$:
To find the derivative, we apply the rules of differentiation.
1. The... show full transcript
Worked Solution & Example Answer:Differentiating the function $f(x) = x - rac{1}{2}(x + 6)^{rac{1}{2}}$ with respect to $x$:
To find the derivative, we apply the rules of differentiation - Leaving Cert Mathematics - Question b, c - 2015
Step 1
Differentiate $x - rac{1}{2}(x + 6)^{rac{1}{2}}$ with respect to $x$
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The derivative f′(x) is calculated as follows:
f'(x) = 1 - rac{1}{2(x + 6)^{rac{1}{2}}}
Step 2
Find the co-ordinates of the turning point of the function $y = x - rac{1}{2}(x + 6)^{rac{1}{2}}$, $x \geq -6$
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Setting the derivative to 0:
0 = 1 - rac{1}{2(x + 6)}
Solving gives:
x = -rac{11}{2}
Now substituting back to find y:
y = -rac{11}{2} - rac{1}{2 ext{(}rac{1}{2} ext{)}}
The coordinates of the turning point are ext{(}-rac{11}{2}, -5 ext{)}.
Join the Leaving Cert students using SimpleStudy...