In Exercises 19–24, calculate the average rate of change of the given function f over the intervals
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Applied Calculus
- In Exercises 11–18, find the slope of the function's graph at the given point. Then find an equation for the line tangent to the graph there. 16. h(t) = t³ + 3t, (1, 4) 18. f(x) = Vx + 1, (8,3)arrow_forwardWhich of the functions graphed in Exercises 1–6 are one-to-one, and which are not?arrow_forwardIn Exercises 7–12, find the indicated derivatives. dr if r = s – 2s? + 3 8. dsarrow_forward
- Suppose that during the period 1990–2001, U.S. imports of pasta increased from 300 million pounds in 1990 (t = 0) by an average of 35 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b)Use your model to estimate U.S. pasta imports (in millions of pounds) in 2006, assuming the import trend continued. _________million poundsarrow_forwardSuppose that during the period 1990–2001, U.S. imports of pasta increased from 270 million pounds in 1990 (t = 0) by an average of 50 million pounds/year. (a) Use these data to express q, the annual U.S. imports of pasta (in millions of pounds), as a linear function of t, the number of years since 1990. q(t) = (b) Use your model to estimate U.S. pasta imports (in millions of pounds) in 2003, assuming the import trend continued.arrow_forward11–24, find the constant of variation for each of the stated conditions. y varies inversely as x, and y= -4 when x= 1/2 . Kaufmann, Jerome E.; Schwitters, Karen L.. Intermediate Algebra (p. 487). Cengage Learning. Kindle Edition.arrow_forward
- Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?arrow_forwardIn Exercises 73–78, the graph of f is shownin the figure. Sketch a graph of the derivative of f. To print anenlarged copy of the graph, go to MathGraphs.com.image5arrow_forwardFind the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forward
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