For \( f(x) = 2x^2 + 1 \), use the definition of the derivative \( f'(x) = \lim_{{h \to 0}} \frac{f(x+h) - f(x)}{h} \) to find \( f'(x) \). - \( f'(x) = 4x \) - \( f'(x) = 2x - 1 \) - \( f'(x) = 4x - 1 \) - \( f'(x) = 2x + 1 \)

Use the definition of derivative to find f'(x) and f"(x). f(x) = 5x2 + 4x + 1 f'(x) f"(x)

f(x)=e^4x

An oil company models the income derived from the continuous production of oil as a continuous income stream using a function f(t), where f(t)=200e^−0.1t, in thousands of dollars per year, where t is in years. Calculate the total income derived from pumping oil after 3 years.   Give your answer in thousands of dollars to the nearest thousand dollars. Do not include commas or the dollar symbol in your answer.