Kinematic Analysis Help Handout

Find the second derivative and simplify ify=25x+16Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

A fast-food restaurant has determined that the monthly demand for its product is given byp=2500-5xp=2500-5xa) Find the revenue functionb) Find the marginal revenue functionc) Find the marginal revenue when x=150Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Differentiate each of the following, be sure to simplifya)f(x)=8x-4×2+9f(x)=8\sqrt{x}-4x^2+9b) f(x)=10×3-18x239f(x)=\frac{10\sqrt{x^3}-18\sqrt[3]{x^2}}{9}c) f(x)=92×4+5x5f(x)=\frac{9}{2x^4} + \frac{5}{x^5}Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

A company is increasing the production of a product at a rate of 30 units per week.  The profit in dollars for the product is given by  P(x)=0.01×2+20x-3000P(x)=0.01x^2+20x-3000where x is the number of units produced.  Find the rate of the change of the profit with respect to time (in dollars per week) when weekly sales are 550 units.Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Alan is 15 miles west of Bob.  Alan runs north at 5 miles per hour.  Bob runs east at 7 miles per hour.  How fast is the distance between the runners changing 3 hours later? Screenshot 2026-02-19 154942.png Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Sketch and find the area of the region bounded by the curvesf(x)=8-x2f(x)=8-x^2g(x)=2x+5g(x)=2x+5Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Integrate each of the followinga) ∫042ex/4 dx \int_0^4 2e^{x/4} \, dx b) ∫14x-2xdx \int_1^4 \frac{x-2}{x}dx Give exact answers do not round or give decimal answers.  Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Integrate each of the followinga) ∫(4x-2)6 dx \int (4x-2)^6 \, dx b) ∫x2(x3-5)2 dx \int \frac{x^2}{(x^3-5)^2}\, dx Upload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.

Integrate each of the followinga) ∫11+6x dx \int \frac{1}{1+6x}\, dx b) ∫2×3+5x-8×4 dx \int \frac{2x^3+5x-8}{x^4}\, dxUpload a picture of your solution with all relevant work.  Make sure your image is clear and readable.  Submit a jpg, jpeg, or png file.  I will not accept pdf or heic files.