Let f (x) be a function that is differentiable everywhere and has a derivative f'(x) = 3x² + 14x + 6. Verify that the Intermediate Value Theorem for Derivatives applies to the function f' (2) on the interval
[-6, -3], and find the value of c guaranteed by the theorem such that f' (c) = -2

I also attached the work that I've done so far, but I don't think that it's right.

Jonathan pays $1.90 per pound for potatoes. he buys 8.3 pounds of potatoes. he determines that he will pay $15.77, before tax, for the potatoes. which best describes the reasonableness of jonathan’s solution? jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product. jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product. jonathan’s answer is reasonable because is 16, and 16 is close to 15.77. jonathan’s answer is unreasonable because is 8, and 8 is not very close to 15.77.

What is the solution to the equation e3x=12? round your answer to the nearest hundredth

A3cm×3cm\greend{3\,\text{cm} \times 3\,\text{cm}} 3cm×3cm start color greend, 3, space, c, m, times, 3, space, c, m, end color greend rectangle sits inside a circle with radius of 4cm\blued{4\,\text{cm}} 4cm start color blued, 4, space, c, m, end color blued . what is the area of the shaded region? round your final answer to the nearest hundredth.