x20 Sx) = tixi. [x). x< 0.

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A: Q 8 Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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Q: For the function f(x) 5x3 – 8x? + 8x, Step 2 of 2: Find the equation of the tangent line at x = 1

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A: To differentiate the given function :

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Q: For what values of x does the graph of f(x) = 2x³ – 9x? – 60x – 3 have a horizontal tangent line?…

A: Given,          fx=2x3-9x2-60x-3 have a horizontal tangent line.

Q: y = (e* + 1)*

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Q: For what values of x does the graph of f (x) =x3 – x² +3 have a horizontal tangent? O 2 O and 2 O O…

A: ⚛ Slope is the rate of change of function which is equal tot he derivative of  that function. ⚛  The…

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Q: Find the indicated derivative for the function. -6 h''(x) for h(x) = 9x - 9x h'(x)=

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Q: Find the equation of the line tangent to the graph of f (x) = 1+ e-*for a. x = 0 b. x = -1

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Q: Find the derivative for each function: h(x) = e ^ ( - x^2 / 2 )

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Q: -2x Answer the following questions about the function whose derivative is f'(x) = (x+5) e2x,

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: