What is the derivative of 𝑓(x)= x 3 ?
Correct!
Wrong!
The power rule for differentiation states that if 𝑓(x)= xn , then 𝑓′(𝑥) = 𝑛𝑥𝑛−1
Evaluate the limit: lim𝑥→2 (3𝑥+1)
Correct!
Wrong!
Substituting x=2 into the function gives 3(2)+1=7.
What is the integral of 𝑓 (x)=2x?
Correct!
Wrong!
The integral of 2𝑥 is found using the power rule for integration, which gives ∫2x dx = x2+C.
What is the second derivative of 𝑓 (𝑥) = 𝑥4?
Correct!
Wrong!
The first derivative of x 4 is 4𝑥3 and the second derivative is 12x 2
Find the critical points of 𝑓 (𝑥) =𝑥 3−3𝑥2
Correct!
Wrong!
"he critical points are found by setting the first derivative equal to zero.
f ′ (x) = 3x 2 −6x = 3x (x−2). Setting this to zero gives 𝑥 = 0
x=2."