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a. Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = ab. Find equations of the tangent lines at the points (1, 5) and (2, 3)Graph the curve and both tangents on a common screen.C.

Question
a. Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = a
b. Find equations of the tangent lines at the points (1, 5) and (2, 3)
Graph the curve and both tangents on a common screen.
C.
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a. Find the slope of the tangent to the curve y = 3 + 4x2 - 2x3 at the point where x = a b. Find equations of the tangent lines at the points (1, 5) and (2, 3) Graph the curve and both tangents on a common screen. C.

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Step 1

Given curve is,

 

2r
y 3+4x
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2r y 3+4x

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Step 2

a). The slope of the tangent is the derivative of the given curve at the given point x = a.

    Therefore,

 

dy
=8x - 6x2
dx
dy
=8a-6a 2a (4-3a)
.Slope of the tangent to the curve y 3+4x2- 2x2 at x = a is 2a(4-3a)
1
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dy =8x - 6x2 dx dy =8a-6a 2a (4-3a) .Slope of the tangent to the curve y 3+4x2- 2x2 at x = a is 2a(4-3a) 1

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Step 3

b). given points are ( 1, 5) and (2, 3).

   First we find the slope of the ta...

dy
8(1)-6(1)8-6=2
dr
..Slope of the tangent to the curve y = 3+4x2 -2x' at (1,5) is 2.
dy
And
8(2)-6(2)16-24 -8
. Slope of the tangent to the curve y 3+ 4x2 -2x' at (2,3) is - 8.
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dy 8(1)-6(1)8-6=2 dr ..Slope of the tangent to the curve y = 3+4x2 -2x' at (1,5) is 2. dy And 8(2)-6(2)16-24 -8 . Slope of the tangent to the curve y 3+ 4x2 -2x' at (2,3) is - 8.

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Calculus

Derivative

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