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2 years ago

(a)Use differentiation to find the minimum value of f(x)= 3x^2 - 5x + 10 and the value(s) of x for which this minimum occurs.

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

3 0

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.

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4 x ((-4)= (-2) - (-3) + (-6))

sergij07 [2.7K]

Answer:

x=5/16

Step-by-step explanation:

Let's solve your equation step-by-step.

4x(−4)=−2−(−3)−6

Step 1: Simplify both sides of the equation.

4x(−4)=−2−(−3)−6

−16x=−2+3+−6

−16x=(−2+3+−6)(Combine Like Terms)

−16x=−5

Step 2: Divide both sides by -16.

−16x

−16

=−5/−16

x=5/16

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2 years ago

Given: F(x) = 5x - 6 and G(x) = x - 4

fomenos

Answer:

Correct choice is $\dfrac{x+26}{5}$

Step-by-step explanation:

1. If $F(x)=5x-6,$ then you can find the inverse $F^{-1}(x):$

$y=5x-6,\\ \\5x=y+6,\\ \\x=\dfrac{y+6}{5},\\ \\F^{-1}(x)=\dfrac{x+6}{5}.$

2. If $G(x)=x-4,$ then

$y=x-4,\\ \\x=y+4,\\ \\G^{-1}(x)=x+4.$

3. Hence,

$G^{-1}(F^{-1}(x))=G^{-1}\left(\dfrac{x+6}{5}\right)=\dfrac{x+6}{5}+4=\dfrac{x+26}{5}.$

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