Question

quiz 10 - requires respondus lockdown browser + webcam
started oct 27 at 9:30pm
quiz instructions
access code: start
timed: 25 minutes
number of attempts: 1
lockdown browser and respondus monitor required.
this quiz covers material from this week: section 3.9
question 5
find f.
f(x) = 18x + 36x²
○ f(x) = 6x³ + 4x⁴ + cx + d
○ f(x) = 4x³ + 8x⁴ + cx + d
○ f(x) = x³ + 4x⁴ + cx + d
○ f(x) = 2x³ + x⁴ + cx + d
○ f(x) = 3x³ + 3x⁴ + cx + d

Explanation:

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

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

Answer:

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