f(x) = 5x(power of 3) - 4x - x(power of 5)?

Question

1. Draw your solution on a graph paper.
*Leading Coefficient Test
*Determine the number of turning points
*Determine where the graph touches or crosses the
x-axis

-using zero of multiplicity k
*x-intercepts
*y-intercepts

Answer 1

I assume the equation you have is y=5x^3 -4x –x^5
To find x intercept set y=0 so you have
5x^3 -4x –x^5=0
x(-x^4 +5x^2 –x^4)=0
x1=0
x1,2,3,4- solve solving
x^4 -5x^2 + 4=0
let u=x^2 and x=+-(sqrt(u))

u^2 – 5u + 4=0
(u-4)(u-1 )=0

x1,2=+- sqrt(4)=+- 2
x3,4=+- sqrt(1)=+-1

1. Apply the Leading Coefficients Test. Because the leading coefficient is negative and the degree is odd, we know that the graph fall on the left and rises on the right.

2. 4 - turning points between (-4,0), (-2,0), (0,0), (2.0), (4,0)

3. X-intercepts are computed above.

4. It crosses the Y-Axis only at x=0 at (0,0).

Answer 2

This quadratic equation occurs to be factorable. maximum are not of direction. the way i like to factor is thru grouping in that 4 words are made from 3. that's carried out with the aid of increasing the midsection term. step a million Multiply the main suited coefficient with the aid of the final quantity the consistent. to that end that's -a million x 5 = -5 step 2 seek for pairs of numbers, that as quickly as expanded, equals this quantity, -5. There are in basic terms 2 opportunities: -a million x 5, or a million x -5 step 3 %. the pair of components above that, whilst extra or subtracted, equals the fee of the coefficient of the midsection term. to that end, the midsection term is +4x and the coefficient is obviously +4 as quickly as we upload -a million to +5 we get this midsection term quantity 4 step 4 Rewrite the equation from 3terms to 4 words with the aid of increasing the midsection term into 2 words. -x^2 +4x +5 = 0 turns into -x^2 -1x + 5x + 5 =0 the two equations are rather an identical superb suited? different than, we've 4 words so as that we are able to factor each and every pair as shown interior the subsequent step step5 separate each and every pair of components: -x^2 - x + 5x +5 = 0 factor each and every pair of words like so: -x(x + a million) +5(x + a million) = 0 step6 now with the aid of utilizing a trick based on the regulation of distribution (i think of it rather is called) we are able to simplify and get our pair of components which equivalent 0. right that's the trick: observe that there is an identical fee in the two bracketed components above? The (x+a million) looks two times superb suited? in case you spot this take place, you recognize you probably did the math wisely! in any case, in simple terms write down between the repeating components (x+a million) and combine the left over numbers by using fact the different factor: (x+a million)(5 - x) = 0 The final step is to unravel for x, with the aid of letting each and every factor (in its turn) be equivalent to 0. Aftr doing this little bit of artwork we get the answer set x = -a million or x = 5

Answer 3

The derivative f'(x) = 15x²-4-5x²x²
So if X= x² f'(x) = -5X²+15X-4
f'(x) =0 for X1= 2.7 and X2 = 0.30
so x1=-1.64, x2= -0.54 x3=0.54 x4=1.64
At the minus infinite f(x) is minus infinite and for the infinite f(x) is infinite
SO it crease from minus infinite to -1.64 then decrease to -0.54 then crease to 0.54 then decresase to 1.64 then crease to the infinite

4 turning points
It cross the x axis at x=1 f(x) =0
it cross the y axis at 0

Answer 4

duhhhhh~ now where did I put my thinking cap..