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Xelga [282]
3 years ago
15

Find the indicated functional value for the floor function: f(−0.75)f(−0.75)?

Mathematics
1 answer:
nikdorinn [45]3 years ago
6 0

We need to find the function value of floor function

Floor function comes under integer functions. we have floor and ceiling function.

Ceiling function gives the least integer value greater than or equal to x.

Floor function gives the greatest integer values less than or equal to x.

For example Celing(3.8) = 4

floor (3.8)= 3

Like that floor f(-0.75) = -1

greatest integer value less than -0.75 is -1

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Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes
ArbitrLikvidat [17]

Complete Question

Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x = 3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ​?

Answer:

The  generally expression for the slope of y  = 2x^2 + 4x is  y' =  4x +4

The graph is shown on the first uploaded image

The  generally expression for the slope of y=2x^2+4 is   y' =  4x

Step-by-step explanation:

From the question we are told that

  The  equation of the curve is y  = 2x^2 + 4x

First we differentiate the equation

So  

     y' =  4x +4

Therefore the generally expression for the slope tangent to the curve y=2x^2+4x is   y' =  4x +4

The  next step is to substitute for x =  3 and  x =  0.5

So  for x_1 =  3

    y' =  4(3) +4

     y' =m_1=  16

And  for  x_2 =  0.5

      y' =  4(0.5) +4

       y' =m_2=  6

Here m_1  and  m_2 are slops of the curve

Next we obtain the coordinates of the tangent lines

So  at x_1 =  3

   y_1  = 2(3)^2 + 4(3)

  y_1  =  21

So the coordinate for the first tangent line is  

    (x_1 , y_1 ) =  (3 ,  21)

At  x_2 = 0.5      

    y_2  = 2(0.5)^2 + 4(0.5)

=>  y_2  = 2.5

So the coordinate for the second  tangent line is  

    (x_2 , y_2 ) =  (0.5 ,  2.5)

Next we obtain the equation for the tangent lines

 So generally the slope is mathematically represented as

        m  =  \frac{y - y_1 }{x-x_1}

For   (x_1 , y_1 ) =  (-3 ,  21) and  y' =m_1=  16

       16 =  \frac{y -21 }{x-3)}

=>    y   = 16x - 27

For  (x_2 , y_2 ) =  (0.5 ,  2.5) and  y' =m_2=  6

       6  =  \frac{y -2.5 }{x-0.5}

       y  = 6x -0.5

Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating  y=2x^2+4 as follows

     y' =  4x

     

7 0
3 years ago
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