quiz 10 - requires respondus lockdown browser + webcam\nstarted oct 27 at 9:30pm\nquiz instructions\naccess…

quiz 10 - requires respondus lockdown browser + webcam\nstarted oct 27 at 9:30pm\nquiz instructions\naccess code: start\ntimed: 25 minutes\nnumber of attempts: 1\nlockdown browser and respondus monitor required.\nthis quiz covers material from this week: section 3.9\nquestion 5\nfind f.\nf(x) = 18x + 36x²\n○ f(x) = 6x³ + 4x⁴ + cx + d\n○ f(x) = 4x³ + 8x⁴ + cx + d\n○ f(x) = x³ + 4x⁴ + cx + d\n○ f(x) = 2x³ + x⁴ + cx + d\n○ f(x) = 3x³ + 3x⁴ + cx + d

quiz 10 - requires respondus lockdown browser + webcam\nstarted oct 27 at 9:30pm\nquiz instructions\naccess code: start\ntimed: 25 minutes\nnumber of attempts: 1\nlockdown browser and respondus monitor required.\nthis quiz covers material from this week: section 3.9\nquestion 5\nfind f.\nf(x) = 18x + 36x²\n○ f(x) = 6x³ + 4x⁴ + cx + d\n○ f(x) = 4x³ + 8x⁴ + cx + d\n○ f(x) = x³ + 4x⁴ + cx + d\n○ f(x) = 2x³ + x⁴ + cx + d\n○ f(x) = 3x³ + 3x⁴ + cx + d

Answer

Explanation:

Step1: Integrate (f''(x)) to find (f'(x))

Use the power rule (\int x^n dx=\frac{x^{n + 1}}{n+1}+C) ((n\neq - 1)). For (y = 18x+36x^{2}), (\int(18x + 36x^{2})dx=18\times\frac{x^{2}}{2}+36\times\frac{x^{3}}{3}+C) (f'(x)=9x^{2}+12x^{3}+C)

Step2: Integrate (f'(x)) to find (f(x))

Again, use the power rule (\int x^n dx=\frac{x^{n + 1}}{n+1}+D) ((n\neq - 1)). (\int(9x^{2}+12x^{3}+C)dx=9\times\frac{x^{3}}{3}+12\times\frac{x^{4}}{4}+Cx + D) (f(x)=3x^{3}+3x^{4}+Cx + D)

Answer:

(f(x)=3x^{3}+3x^{4}+Cx + D) (the fifth option)