The curve $$y=ax3+bx2+cx+8$$ touches $$x-axis$$ at $$P($$−$$2$$,$$0)$$ and cuts the $$y-axis$$ at a point Q where its gradient is $$3$$. The values of a, b, c are respectively

Question

The curve $$y=ax3+bx2+cx+8$$ touches $$x-axis$$ at $$P($$−$$2$$,$$0)$$ and cuts the $$y-axis$$ at a point Q where its gradient is $$3$$.    The values of a, b, c are   respectively

Infinity Learn · Accepted Answer

$$dydx=3ax2+2bx+c$$ Since the curve touches $$x-axis$$ at $$($$−$$2$$,$$0)$$ so $$dydx($$−$$2$$,  $$0)$$  $$=$$   $$0$$ ⇒  $$12a$$ − $$4b$$ $$+c$$  $$=$$  $$0----iThe$$ curve cut the $$y-axis$$ at (0$$, $$8)  $$sodydx($$  $$0$$,   $$8)$$  $$=$$   $$3$$ ⇒  c  $$=$$  $$3$$ Also the curve passes through $$($$−$$2$$,$$0)$$ so $$0=$$−$$8a+4b$$−$$2c+8$$⇒−$$8a+4b$$−$$2=0----ii$$ Solving (i) and  (ii) $$a=$$−$$1/4$$,$$b=0$$

$The curve y = a x^{3} + b x^{2} + c x + 8 touches x -axis at P (- 2, 0) and cuts the$ $y-axis at a point Q where its gradient is 3. The values of a, b, c are respectively$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The curve y=ax3+bx2+cx+8 touches x-axis at P(−2,0) and cuts the y-axis at a point Q where its gradient is 3. The values of a, b, c are respectively

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

$The curve y = a x^{3} + b x^{2} + c x + 8 touches x -axis at P (- 2, 0) and cuts the$ $y-axis at a point Q where its gradient is 3. The values of a, b, c are respectively$