Suppose that the only information we have about a function fis that f1)9 and the

Question

Suppose that the only information we have about a function fis that f1)9 and the graph of its derivative is as (a) Use a linear approximation to estimate to.95) 0.95) and K 1.05). - The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too smail - The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f Thus, the estimates The slopes of the tangent lines are negative, but the tangents are becoming steeper So the tangent lines le below the curve f. Thus, the estimates are too lurge The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve r. Thus, the

Explanation / Answer

We are given
f(1) = -9
And f'(1) = 2

So, using linear approx formula
f(x) = f(a) + f'(a)*(x - a)

f(x) = f(1) + f'(1)*(x - 1)

f(x) = -9 + 2(x - 1)

f(x) = 2x - 11

Now, plug in x = 0.95 and 1.05 :
f(0.95) = 2(0.95) - 11 -----> -9.1 -----> ANS

f(1.05) = 2(1.05) - 11 -----> -8.9 ----> ANS

--------------------------------------------------------------------

b)
Clearly the graph given is the derivative graph....

And all valus are positive

So, either option B or D

This grpah will be concave down as derivatives are decreasing

And thus, overestimate

Option D

----------------------------------------------------------------------

11)
dV/dt = 2 m^3/min
radius, r = 3 m

d/dt(pi*r^2*h) = 2

pi*r^2 * dh/dt

pi * 3^2 * dh/dt = 2

dh/dt = 2/(9pi)

= 0.0707 meter/min ----> ANS

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.