Question

Let h be a differentiable function with a tangent line at x = π. The equation of the tangent line is y = -0.2x + 0.5. What must be true about h and h' at x = π?

Answer 1

The value of h(π) is 0.5 and the value of h'(π) is -0.2.

Step-by-step explanation:

Slope of the tangent line at x = π:

The equation of the tangent line at x = π is y = -0.2x + 0.5. The slope of the tangent line at a point is equal to the derivative of the function at that point. Therefore, h'(π) = -0.2.

Y-intercept of the tangent line:

The y-intercept of the tangent line is 0.5. The y-intercept of a tangent line represents the function value at the point of tangency. Therefore, h(π) = 0.5.

Therefore, both h(π) = 0.5 and h'(π) = -0.2 must be true about h and h' at x = π.