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Hand draw a tangent line to the graph at each x-component given below. Use these

ID: 3288294 • Letter: H

Question

Hand draw a tangent line to the graph at each x-component given below. Use these tangent lines to estimate the value of each derivative. Write your estimate beside each question. Using your estimates from part (a), draw the graph of f (x) on the same set of axes given above. Please use a different color of ink from your tangent lines. Shown is the graph of the population function P(t) for yeast cells in a laboratory culture. Use the method above to draw the graph of P (t) on the same set of axes given. What does P (t) represent? Describe how the rate of population increase varies over time. When is this rate highest?

Explanation / Answer

f'(-3)= 2,

f'(-2)=1,

f'(-1)=0,

f'(0)=-2,

f'(1)=0,

f'(2)=1,

f'(3)=2


ii. The rate at which the population is growing (negative means population is decreasing)

iii. As time goes on, growth slows, decreases a little bit then levels off. This happens when the population runs out of resources.

iii. 7.5 hours