1. Equal derivatives Verify

that the functions 1×2

=

tan2 x and g1x2

=

sec2 x have

the same derivative. What can you say about the difference –

g?

Explain. 50.

100-m speed The Jamaican sprinter Usain Bolt set a world record

of 9.58 s in the 100-meter dash in the summer of 2009. Did his speed ever

exceed 37 kmhr

during the race? Explain.

2. Condition for nondifferentiability Suppose

_1x2

6

0

6

_1x2, for

x

6

a, and

_1x2

7

0

7

_1x2, for

x

7

a.

Prove that

is

not differentiable at a. (Hint:

Assume

is

differentiable at a, and apply the Mean Value

Theorem to _.)

More generally,

View complete question »

1. Equal derivatives Verify

that the functions 1×2

=

tan2 x and g1x2

=

sec2 x have

the same derivative. What can you say about the difference –

g?

Explain. 50.

100-m speed The Jamaican sprinter Usain Bolt set a world record

of 9.58 s in the 100-meter dash in the summer of 2009. Did his speed ever

exceed 37 kmhr

during the race? Explain.

2. Condition for nondifferentiability Suppose

_1x2

6

0

6

_1x2, for

x

6

a, and

_1x2

7

0

7

_1x2, for

x

7

a.

Prove that

is

not differentiable at a. (Hint:

Assume

is

differentiable at a, and apply the Mean Value

Theorem to _.)

More generally, show that if _ and _ change

sign at the same point, then is not

differentiable at that point.

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