Question

3 mark for review an equation of the line tangent to the graph of y = x+cos x at the point (0,1) is a y = 2x + 1 b y = x + 1 c y = x d y = x - 1 e y = 0

Explanation:

Step1: Find the derivative of the function

The derivative of $y = x+\cos x$ is $y'=1 - \sin x$.

Step2: Evaluate the derivative at the given x - value

When $x = 0$, $y'(0)=1-\sin(0)=1$. The value of the derivative at $x = 0$ is the slope $m$ of the tangent line.

Step3: Use the point - slope form of a line

The point - slope form is $y - y_1=m(x - x_1)$. Here, $x_1 = 0$, $y_1 = 1$ and $m = 1$. Substituting these values gives $y - 1=1\times(x - 0)$, which simplifies to $y=x + 1$.

Answer:

B. $y=x + 1$