Answer:
D
Step-by-step explanation:
g(x)=f(5x)
this means plugging in 5x for x in f(x):
g(x)=f(5x)=(5x)^2
which can be further simplified:
5^2x^2=25x^2
Since the coefficient of x being larger means a vertical stretch, the answer is D
example:
g(2)=f(5*2)=f(10)=f(10^2)=100
so for g(x), it has the coordinates (2,100), which is most definitely not C
The point of inflection is calculated by equating the second derivative to zero and determining x from there.
f"(x) = -x²2xsinx² + cosx²(2x) = 0
2xcosx² - 2x³sinx² = 0
2x (cosx² - xsinx²) = 0
2x = 0 ⇒ x = 0
cosx² - xsinx² = 0 ⇒ x = 3.82 (if you use shift+solve in your scientific calculator)
Thus, the function only has 1 point of inflection and it is at x = 0.
