F is a function that is differentiable for all reals. The value of f '(x) is given for several values of x in the table below. x -8 -3 0 3 8
f '(x) 5 4 0 -2 -4
If f '(x) is always decreasing, which statement about f(x) must be true?

a.
f(x) has a relative maximum at x = 0.

b.
f(x) is concave upwards for all x.

c.
f(x) has a point of inflection at x = 0.

d.
f(x) passes through the origin.

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  a.  f(x) has a relative maximum at x = 0.

Step-by-step explanation:

Since f' is decreasing, the second derivative is negative. That means the graph is concave downward, so any critical point is a relative maximum.

  f(x) has a relative maximum at x=0 (where f'(0) = 0)

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There is no indication that the second derivative is ever zero, so there is no point of inflection.

No values of f(x) are given, so we cannot say whether the function passes through the origin.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.