Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

$f'(c) = \frac{f(b)-f(a)}{b-a}$

So, for the function f(x) = $2x^{3}-9x^{2}-60x+1$ on interval [-4,9]

$f'(x) = 6x^{2}-18x-60$

f(-4) = $2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1$

f(-4) = 113

f(9) = $2.(9)^{3}-9.(9)^{2}-60.(9)+1$

f(9) = 100

Calculating average:

$6c^{2}-18c-60 = \frac{100-113}{9-(-4)}$

$6c^{2}-18c-60 = -1$

$6c^{2}-18c-59 = 0$

Resolving through Bhaskara:

c = $\frac{18+\sqrt{1740} }{12}$

c = $\frac{18+41.71 }{12}$ = 4.97

c = $\frac{18-41.71 }{12}$ = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97

7 0

3 years ago

(c³d)a(cd⁷)a Simplify

Veseljchak [2.6K]

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

5 0

3 years ago

107+0+39+13 use properties to fin the sum

Vikentia [17]

The answer to the question is 159 all you do is add everything together

6 0

4 years ago

Which expression can be used to determine 50% of 42? 42 minus 2 42 divided by 2 42 divided by 10 42 minus 10

Mrrafil [7]

Answer:

We know that 50% of 42 will be = 21

i.e. 50% of 42 = 50/100 = 21

The correct answer should be: 42 divided by 2

Step-by-step explanation:

We know that 50% of 42 will be = 21

i.e. 50% of 42 = 50/100 = 21

Also, when we divide 42 by 2, we get the answer 21.

i.e. 42/2 = 21

Therefore, the correct answer should be: 42 divided by 2

5 0

3 years ago

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