Question 3:
The straight line y = 5x – 1 does not intersect with the curve y = 2x2 + x + h.
Find the range of values of h.
Solution:
y=5x−1 ...... (1)y=2x2+x+h ...... (2)Substitute (1) into (2),5x−1=2x2+x+h2x2+x+h−5x+1=02x2−4x+h+1=0 b2−4ac<0(−4)2−4(2)(h+1)<0 16−8h−8<0 8<8h h>1
The straight line y = 5x – 1 does not intersect with the curve y = 2x2 + x + h.
Find the range of values of h.
Solution:
y=5x−1 ...... (1)y=2x2+x+h ...... (2)Substitute (1) into (2),5x−1=2x2+x+h2x2+x+h−5x+1=02x2−4x+h+1=0 b2−4ac<0(−4)2−4(2)(h+1)<0 16−8h−8<0 8<8h h>1
Question 4:
Find the maximum value of the function 5 – x – 2x2 , and the corresponding value of x.
Solution:
5−x−2x2=−2x2−x+5=−2[x2+12x−52]=−2[x2+12x+(14)2−(14)2−52]=−2[(x+14)2−116−52]=−2[(x+14)2−4116]=−2(x+14)2+518
5−x−2x2 has a maximum value when2(x+14)2=0 x=−14The maximum value of 5−x−2x2 is 518.
Find the maximum value of the function 5 – x – 2x2 , and the corresponding value of x.
Solution:
5−x−2x2=−2x2−x+5=−2[x2+12x−52]=−2[x2+12x+(14)2−(14)2−52]=−2[(x+14)2−116−52]=−2[(x+14)2−4116]=−2(x+14)2+518
5−x−2x2 has a maximum value when2(x+14)2=0 x=−14The maximum value of 5−x−2x2 is 518.