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Nuetrik [128]
3 years ago
12

Evaluate F(1)

Mathematics
1 answer:
KonstantinChe [14]3 years ago
8 0

ANSWER

B. 1

EXPLANATION

The given function is

f(x) =\left \{ {{x^{2} +3 (if) -5 \leq x< 1} \atop {x (if) 1 \leq x \leq 5 }} \right.

This is a piece-wise defined function.

We want to find f(1)

We substitute x=1 into f(x)=x because, 1 belongs to the interval,

1≤x≤5

f(1)=1

The correct answer is B.

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A bakery will make 5,400 graham crackers. The graham crackers are packaged in boxes of 60. How many boxes of graham crackers wil
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How do you find the value of c that satisfy the equation:
victus00 [196]

Answer:

The value of c = -0.5∈ (-1,0)

Step-by-step explanation:

<u>Step(i)</u>:-

Given function f(x) = 4x² +4x -3 on the interval [-1 ,0]

<u> Mean Value theorem</u>

Let 'f' be continuous on [a ,b] and differentiable on (a ,b). The there exists a Point 'c' in (a ,b) such that

f^{l} (c)  = \frac{f(b) -f(a)}{b-a}

<u>Step(ii):</u>-

Given  f(x) = 4x² +4x -3 …(i)

Differentiating equation (i) with respective to 'x'

          f¹(x) = 4(2x) +4(1) = 8x+4

<u>Step(iii)</u>:-

By using mean value theorem

f^{l} (c)  = \frac{f(0) -f(-1)}{0-(-1)}

8c+4 = \frac{-3-(4(-1)^2+4(-1)-3)}{0-(-1)}

8c+4 = -3-(-3)

8c+4 = 0

8c = -4

c = \frac{-4}{8} = \frac{-1}{2} = -0.5

c ∈ (-1,0)

<u>Conclusion</u>:-

The value of c = -0.5∈ (-1,0)

         

<u></u>

8 0
3 years ago
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