77 Which one of the following could be the graph of a polyno

77. Which one of the following could be the graph of a polynomial of degree 4 with a negative leading coefficient?

Solution

Since a quartic polynomial function can be generally represented as

f(x)= ax+bx³+cx²+dx+e

Now if the leading coefficient that is coefficient of maximum power of x is negetive that the f(x) value will be negetive for all x in the range of minus infinity to positive infinity

Thus f(x) will always be at negitive infinity for either equals +infinity or -infinity so the graph will be option C

If the leading coefficient is positive than f(x) will always be infinte for x either +infinity or -infinity thus for that D is correct