Calculas

Question 1

y=4x(pwr5)+6x(pwr4)+3x(pwr3)+5x(pwr2)+10x+1

Answer 1

dy=20x(pwr4)+24x(pwr3)+9x(pwr2)+10x+10
dx .

Question 2

y=(3x(pwr2)+1) (2x-4)

Answer 2

dy= 3x(pwr2)+1(2)+2x-4(6x)
dx .

Question 3

Differentiate x(pwr2)+2x from the first principal

Answer 3

f(x+h)-f(x)=2x+h+2
h .

Question 4

y=(3x(pwr2)+2)(pwr5)

Answer 4

y=30x(3x(pwr2)+2)(pwr4)

Question 5

Differentiate the function
y=x(pwr3)-9x(pwr2)+15x+2

Answer 5

Local min= 5,-23
Local max= 1,9
Point on inflection= 3,-7

Question 6

f(x)=ax(pwr3)+bx(pwr2)+cx+d
Max= 0,4
Point of inflection= 1,0
Find a,b,c+d

Answer 6

a=2
b=-6
c=0
d=4

Question 7

f(x)=x(pwr3)+kx(pwr2)-4
Show that the coordinates of local max and local min are (0,-4) and (-2k,4k(pwr3)-108)
3 27 .