The position of an object moving along a line is given by the function s(t) = - 17t +136t. Find the average velocity of the object over the following intervals. (a) [1, 5] (c) [1, 3] (b) [1, 4] (d) [1, 1+h] where h>0 is any real number. .....

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Q: Find f(4) and f'(4), assuming that the tangent line to y = f(x) at a = 4 is y = -7x +2.

A: The derivative of a function at a point represents the slopeof tangent at that point .

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A: By using the derivative and slope intercept form required tangent equation is :

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A: We have find possible point where the slope of the tangent is -1

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A: Now tangent line is horizontal if slope of the tangent line is zero and slope of the tangent line is…

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A: f(x)=(x+4)(3x+3)=x+13(x+1)+33(x+1)=13+1x+1 f'(x)=-1(x+1)2 f''(x)=2(x+1)3 the slope of the tangent at…

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Q: 1. (a). Find the linear approximation to f(x) = VT at r = 81, (b). use it to approximate V85. (c).…

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A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

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A: We have to find

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Q: x4 C: y=-+ 3 x3 17 4 12

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Q: Let f(x) = 1x4 /4 + 2x3 – x2 + 3x + 7.                       a. Find f ’(x).  b. Find the equation…

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Q: Find h'(-2) if h= fog. f(z) = 372 + 8 and the equation of the tangent line of g at-2 is y= 4x 6.

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A: The given function is

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Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

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Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

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A: NOTE: Refresh your page if you can't see any equations. . the given point is  and the given…

Q: 9. Find the point on the graph of y = x² where the tangent line is parallel to the line 3x – 4y = 4.

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Q: Find the average velocity of an object for the interval 1<t< 3, if its position is given by s = = t²…

A: Differentiate the function to find the velocity function. dsdt=2t+5

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Q: Find the equation of the tangent line to the curve f(x)=5-x² at x = 2. O x-4y-2=0 O 4x + y +7=0 O 4x…

A: Find the equation of the tangent line to the curve f(x) =5-x^2 at x=2.

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Q: 3. Find the equation of the tangent line to the graph of x²y + 9xy= 162 at the point (-3, 6).

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.