Prove that the function f(x)=5x^3+4x-23 has exactly one zero.
Answers
Answered by
0
y = 5x³ + 4x - 23 has exactly only one real zero. it means , function cut at x - axis in only one point .
y = 5x³ + 4x - 23
now, differenciate with respect to x
dy/dx = 15x² + 4 > 0
hence, function is always increasing .
e.g one - one function .
it means have not more then one solution ( zero ) .
now, check is function has real solution .
f(1) = 5(1)³ + 4(1) -23 < 0
f(2) = 5(2)³ + 4(2) - 23 > 0
hence, between 1 and 2 must have one real solution of given function .
hence, function has exactly one zero
y = 5x³ + 4x - 23
now, differenciate with respect to x
dy/dx = 15x² + 4 > 0
hence, function is always increasing .
e.g one - one function .
it means have not more then one solution ( zero ) .
now, check is function has real solution .
f(1) = 5(1)³ + 4(1) -23 < 0
f(2) = 5(2)³ + 4(2) - 23 > 0
hence, between 1 and 2 must have one real solution of given function .
hence, function has exactly one zero
Attachments:
Similar questions