#18 differentiate and #19 17) y-2-3x +2 17) x7-2 dy -5x8+19x7 14x6 4x +6 dx -5x8
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#18 differentiate and #19
17) y-2-3x +2 17) x7-2 dy -5x8+19x7 14x6 4x +6 dx -5x8+18x7 14x6 -3x 6 (x7-2)2 -5x8 + 18x7-13x6-4x + 6 (x7-2)2 dx c dy -5x8, 18x7-14x6. 4x 6 dy (x7-2)2 2.2.2 18) y 18) x2 2x 2 -4x2-8x B) d-, -4x2 + 8x dy dx (x2 2x 2) dy 4x2-8x A) dx (x2 2x 2)2 4x2 +8x . dx (x2- 2x 2)2 Write an equation of the tangent line to the graph of y fx) at the point on the graph where x has the indicated val 19) fx) (3x2 - 5x 2)(2x 5), x -0 19) B) y 21x 10 C)y=?-10 D)y=21x + 10 21 21 Solve the problem. 20) An appliance manufacturer has determined that the cost, in dollars, of producing x espresso 20) makers is given by C(x) 38001.6x05. If the revenue from the sale of x espresso makers is given ? ?Explanation / Answer
18) y = (x2 + 2x - 2) / (x2 - 2x + 2)
Differentiating using quotient rule
=> dy/dx = [(2x + 2) (x2 - 2x + 2) - (2x - 2) (x2 + 2x - 2)] / (x2 - 2x + 2)2
= (2x3 - 4x2 + 4x + 2x2 - 4x + 4 - 2x3 - 4x2 + 4x + 2x2 + 4x - 4) / (x2 - 2x + 2)2
= (-4x2 + 8x) / (x2 - 2x + 2)2
The correct answer is B).
19) y = f(x) = (3x2 - 5x - 2) (2x - 5)
When x = 0,
y = (3*0 - 5*0 - 2) (2*0 - 5)
= -2 * -5
= 10.
y = (3x2 - 5x - 2) (2x - 5)
=> y = 6x3 - 10x2 - 15x2 + 25x - 4x + 10
=> y = 6x3 - 25x2 + 21x + 10
Differentiaing with respect to x
=> dy/dx = 18x2 - 50x + 21
At x = 0, dy/dx = 21.
The slope of the tangent is also 21.
The equation is y = 21 x + 10.
This is given in D).
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