Question

question topic(s)/section(s): 2.7 derivatives of cos(x), sin(x), e^x, and ln(x) what is the slope of the line tangent to the graph of y = 3cos(x) at the point where x = π/2? 3 0 -1/2 -3 clear my selection

Explanation:

Step1: Find the derivative of the function

The derivative of $y = 3\cos(x)$ using the constant - multiple rule and the derivative formula for $\cos(x)$ is $y'=- 3\sin(x)$.

Step2: Evaluate the derivative at the given point

Substitute $x = \frac{\pi}{2}$ into $y'$. We know that $\sin(\frac{\pi}{2}) = 1$, so $y'=-3\times1=- 3$.

Answer:

-3