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For the following exercises, draw and label diagrams to help solve the related-rates problems.

The base of a triangle is shrinking at a rate of 1 cm/min and the height of the triangle is increasing at a rate of 5 cm/min. Find the rate at which the area of the triangle changes when the height is 22 cm and the base is 10 cm.

The area of the triangle is increasing at a rate of 14 $\mathrm{cm} / \mathrm{min}$ .

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 1

Related Rates

Applications of the Derivative

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Harvey Mudd College

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We know the formula for the area of a triangle with based B and high age is a equals 1/2 the age differentiating using the product rule. If I split this up into two components 1/2 B and H using the product rule day over DT, I got 1/2 times D B that indicates base times age plus B times D H you can probably in furnace indicates height changing height so h and B just using those with derivatives. You know dp over. Dt is negative. One d h over dt is five. B is 10 and ages 22 So plugging him, we end up with D A over DT equals 14 centimeters per minute.

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